This invention relates, in general, to electrooptical signal processing and, more specifically, to acousto-optic processing of matrix and vector expressions.
Optical processors of various varieties have been disclosed in the prior art for matrix-vector and vector-vector multiplication, with their advantage being primarily in the speed of operation as compared to more typical digital electronic devices. Optical processors which use binary techniques offer better resolution than analog optical processors, which are usually only accurate to within seven to nine bits.
One method of binary optical processing makes use of algorithm of analog convolution and its extension to twos complement arithmetic. This method is based upon multiplying two binary numbers by convolving their bits. The result is in mixed binary form, thus different binary numbers can be added without the need for carries. This method is generally associated with matrices having only real-positive elements. However, extension to complex matrices is possible by partitioning the complex numbers into four unipolar parts. In order to reduce the matrix partitioning, it is helpful to use twos complement binary arithmetic which uses a sign bit for positive and negative numbers. Each binary product, including its sign bit, is represented in a mixed binary form so that different products can be added without the need for carries.
Implementation of the above-described technique based upon electro-optical engagement-array techniques have been proposed by others. However, such techniques require real-time, fast, and reusable two-dimensional reflecting valves which are expensive and in short supply.
Therefore, it is desirable, and it is an object of this invention, to provide a processing system which uses twos complement arithmetic without the hardware requirements of prior art systems.
The paper by R. P. Bocker, et al., published in Applied Optics, July 1983, pages 2019 to 2021, gives a description of twos complement arithmetic as applied to electro-optical matrix multiplication architectures. The paper by D. Casasent, published in The Proceedings of the International Society for Optical Engineering, August 1982, pages 50 to 58, describes acousto-optic processor architecture which is used for vector multiplication. Although similar to the invention disclosed herein, the systems disclosed in the referenced paper do not use a cylindrical lens or other space-integrating member to form the inner product on a single one-dimensional light detector array.